Stratified Hyperbolicity of the moduli stack of stable minimal models, I

2025/06/21 by Shentu, Junchao · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.17537

Abstract

In this paper, we introduce a birationally admissible stratification on the Deligne-Mumford stack of stable minimal models (e.g., the KSBA moduli stack), such that the universal family over each stratum admits a simple normal crossing log birational model. We further demonstrate that each stratum is hyperbolic in the sense that every schematic generically finite covering of any closed substack is of logarithmic general type. This provides a partial answer to C.Birkar's question regarding the global geometry of the moduli of stable minimal models.

Citations

• Stratified Hyperbolicity of the moduli stack of stable minimal models, II: Big Picard Theorem and the stratified Brody hyperbolicity
• Viehweg hyperbolicity for Whitney equisingular families with Gorenstein rational singularities
• Hodge sheaves underlying flat projective families
• Limits of Hodge structures via holonomic D-modules
• Moduli of polarized Calabi-Yau pairs
• Hyperbolicity for log smooth families with maximal variation
• On the Kodaira dimension of base spaces of families of manifolds
• Semi-positivity from Higgs bundles
• Viehweg's hyperbolicity conjecture for families with maximal variation
• Foliations with positive slopes and birational stability of orbifold\n cotangent bundles
• Projectivity of the moduli space of stable log-varieties and subadditvity of log-Kodaira dimension
• Semipositivity theorems for moduli problems
• Variations of mixed Hodge structure and semi-positivity theorems
• Resolution of singularities of pairs preserving semi-simple normal crossings
• Moduli of varieties of general type
• Families of varieties of general type over compact bases
• Families of canonically polarized varieties over surfaces
• Base spaces of non-isotrivial families of smooth minimal models
• On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds
• On the isotriviality of families of projective manifolds over curves
• On the isotriviality of families of elliptic surfaces
• Complete moduli in the presence of semiabelian group action

Cited by

• Stratified Hyperbolicity of the moduli stack of stable minimal models, II: Big Picard Theorem and the stratified Brody hyperbolicity

Related

• Stratified Hyperbolicity of the moduli stack of stable minimal models, II: Big Picard Theorem and the stratified Brody hyperbolicity
• Hyperbolicity of the base of an admissible family of log canonical stable minimal models
• Stable Reduction via the Log Canonical Model
• Moduli spaces of snc klt KSBA stable pairs are naturally of log general type
• Differential forms on singular spaces, the minimal model program, and hyperbolicity of moduli stacks